How do I stop the windows on the weather ends of my log cabin from leaking?

Install a counter piece of flashing, cut into the log at the top piece of the window trim.

Should I pressure wash my log cabin?

Yes, but only by someone with experience of pressure washing and staining log cabins.

Should I fill the checks of my log cabin?

Only if the checks leak water or air.

If the chinking on my cabin is separating at the top and sometimes the bottom, does that mean my logs are shrinking or settling?

No, more than likely it means the chinking isn’t the proper thickness at the top and bottom.  Thickness should be 3/8″ to a 1/2″ inch thick top and bottom, middle thickness should be 1/4″.